The Pinocchio Paradox

Jim Wynne · Apr 22, 2009

While this is essentially not a puzzle, I think it presents an interesting subject for quality people. It's called the Pinocchio Paradox, and is based on the idea that when Pinocchio tells a lie, his nose grows longer (see the attachment). Using the following definition of "paradox" from the American Heritage Dictionary: " An assertion that is essentially self-contradictory, though based on a valid deduction from acceptable premises" is this actually a paradox?

Now, discuss.

Keith Childers · Apr 22, 2009

Jim Wynne said:
While this is essentially not a puzzle, I think it presents an interesting subject for quality people. It's called the Pinocchio Paradox, and is based on the idea that when Pinocchio tells a lie, his nose grows longer (see the attachment). Using the following definition of "paradox" from the American Heritage Dictionary: " An assertion that is essentially self-contradictory, though based on a valid deduction from acceptable premises" is this actually a paradox?

Now, discuss.

Very interesting.

I would say that yes, this is a paradox.
His statement that his nose will grow is self contradictory.
If he is not actually expecting his nose to grow, then he is telling a lie and his nose will grow, however because the lie will cause his nose to grow, he is telling the truth, therefore there is no reason for his nose to grow, which makes his statement a lie...

Miner · Apr 22, 2009

If he told a lie immediately prior to this statement, he could then tell the truth and his nose would still grow. There is no evidence that telling the truth would counteract an initial lie.

Geoff Withnell · Apr 23, 2009

Keith Childers said:
Very interesting.

I would say that yes, this is a paradox.
His statement that his nose will grow is self contradictory.
If he is not actually expecting his nose to grow, then he is telling a lie and his nose will grow, however because the lie will cause his nose to grow, he is telling the truth, therefore there is no reason for his nose to grow, which makes his statement a lie...

This would depend on the definition of a "lie". If a lie is a statement that is believed to be untrue, then when he says his nose will grow, and does not expect it to, it remains a lie, even it his nose does grow, because he believed it would not. If he believes his nose will grow, and says so, then when his nose does not grow, the statement is not then a lie, it is just a mistake, so no paradox.

Geoff Withnell

Jim Wynne · Apr 23, 2009

Geoff Withnell said:
This would depend on the definition of a "lie". If a lie is a statement that is believed to be untrue, then when he says his nose will grow, and does not expect it to, it remains a lie, even it his nose does grow, because he believed it would not. If he believes his nose will grow, and says so, then when his nose does not grow, the statement is not then a lie, it is just a mistake, so no paradox.

Geoff Withnell

Yes, it's not as simple as it seems at first glance. My initial take was that Pinocchio is making a prediction, which shouldn't be necessarily be classified as a lie unless we know that the prediction was knowingly dishonest. Even at that, we're still left with what constitutes a "lie." Is a lie any knowingly dishonest utterance?

iamnototep · Sep 15, 2010

It is just a variation of the sentence, "This statement is false".

A variation which removes the self-referential aspect, sort of, by replacing it with reference to a different sentence which then refers back to the first:
"The following statement is true"
"The preceding statement is false"

Having Pinocchio there just complicates matters.

The Pinocchio Paradox

Jim Wynne

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